Kali is the Filipino ancestral term for the group of arts
developed there. Arnis and Eskrima are both Spanish
influenced terms. As with all the tribal dialects, there
are variations on the details in the different arts.

My guro told me there should be millions of variations,
as each eskrimador should have his own 'expresszion
of the training' to show for the effort put into him and
to honor his guro.

Yes.
This may interest you. . .
He related to me that as a young man he returned to the PI
intending to study Kali/Escrima with a master. He and a friend
searched all over the PI, but were told that most of the kali
masters had fled to California in the US.